Unpredictability From Chance

“How are we to understand “chance,” which Clausewitz finds pervasive? It is one of the three points of attraction in his definition of war as a remarkable trinity, and he emphasizes that “no other human activity is so continuously or universally bound up with chance” as is war.  It is associated also with the fog of uncertainty in war, which obscures or distorts most of the factors on which action is based. Yet he nowhere provides a succinct definition of chance. “

The connection between chance and uncertainty provides a means of understanding both, if we draw on the insights of the late nineteenth-century mathematician Henri Poincaré, whose understanding of the matter was powerful enough that he is a frequently cited source in nonlinear science today. Poincaré argued that chance comes in three guises: a statistically random phenomenon; the amplification of a microcause; or a function of our analytical blindness. He described the first as the familiar form of chance that can arise where permutations of small causes are extremely numerous or where the number of variables is quite large. This form of chance can be calculated by statistical methods. The very large number of interactions produces a disorganization sufficient to result in a symmetrical (i.e., Gaussian or bell curve) probability distribution. Nothing significant is left of the initial conditions, and the history of the system no longer matters. It is possible that Clausewitz was aware of this general line of reasoning. As with magnetism and friction, important developments in probability theory were occurring in Clausewitz’s time, and we know that he read intensely in mathematical treatises.

Of course On War does not present this statistically tractable form of chance in exactly the way Poincaré explained it later, although commentators have noted that Clausewitz often refers to the role of probability in a commander’s calculations. In Chapter 1, Book One, he notes that “absolute, so-called mathematical factors” are not sound bases for such calculations due to the “interplay of possibilities, probabilities, good luck and bad” that are endemic in war. The “games of chance” most amenable to statistical treatment are those like dice and coin tossing, but when Clausewitz compares war to a gamble, he does not use either. For him, “in the whole range of human activities, war most closely resembles a game of cards.” This analogy suggests not only the ability to calculate probabilities, but knowledge of human psychology in “reading” the other players, sensing when to take risks, and so on. Clausewitz certainly understands that the number of variables in war can be enormous, and that a rather special aptitude is needed to cope with the chance and complexity involved:

Circumstances vary so enormously in war, and are so indefinable, that a vast array of factors has to be appreciated — mostly in the light of probabilities [Wahrscheinlichkeitsgesetze] alone. The man responsible for evaluating the whole must bring to his task the quality of intuition that perceives the truth at every point. Otherwise a chaos of opinions and considerations would arise, and fatally entangle judgment. Bonaparte rightly said in this connection that many of the decisions faced by the commander-in-chief resemble mathematical problems worthy of the gifts of a Newton or an Euler. 

Since a mathematician of the likes of Newton or Euler is unlikely to be making military decisions, those in command have to rely on judgment rooted in intuition, common sense, and experience. Statistical laws of probability alone will never suffice, because moral factors always enter into real war, and it is possible for the results of any given action to defy the odds. This is one of the most important facts that experience indeed provides. 

 

A second form of chance described by Poincaré is deeply embedded in On War, but commentators have not usually distinguished its nature from that of the first. In contrast to the statistical form characterized above, this type of chance—amplification of a microcause—is inherent in the system itself. It arises from the fact that in certain deterministic systems small causes can have disproportionately large effects at some later time. Because the history of the system matters, the initial conditions remain significant. In a passage often cited by researchers working on nonlinear dynamics, Poincaré explained:

A very slight cause, which escapes us, determines a considerable effect which we can not help seeing, and then we say this effect is due to chance. If we could know exactly the laws of nature and the situation of the universe at the initial instant, we should be able to predict exactly the situation of this same universe at a subsequent instant. But even when the natural laws should have no further secret for us, we could know the initial situation only approximately. If that permits us to foresee the subsequent situation with the same degree of approximation, this is all we require, [and] we say the phenomenon has been predicted, that is ruled by laws. But this is not always the case; it may happen that slight differences in the initial conditions produce very great differences in the final phenomenon; a slight error in the former would make an enormous error in the latter. Prediction becomes impossible and we have the fortuitous phenomenon.

Poincaré thus linked the crucial importance of the initial conditions to the idea that in the real world the precision of our information concerning causes is always limited. This is a root explanation for unpredictability in those nonlinear phenomena that exhibit chaotic regimes of behavior.

This is exactly how Clausewitz perceives the role of chance in relation to friction in real war. Unnoticeably small causes can be disproportionately amplified. Decisive results can often rest on particular factors that are “details known only to those who were on the spot.” Attempts to reconstruct cause and effect always face the lack of precise information:

Nowhere in life is this so common as in war, where the facts are seldom fully known and the underlying motives even less so. They may be intentionally concealed by those in command, or, if they happen to be transitory and accidental, history may not have recorded them at all.

We can never recover the precise initial conditions even of known developments in past wars, much less developments in current wars distorted by the fog of uncertainty. Interactions at every scale within armies and between adversaries amplify microcauses and produce unexpected macroeffects. Since interaction is intrinsic to the nature of war, it cannot be eliminated. The precise knowledge needed to anticipate the effects of interaction is unattainable. Unpredictability in war due to this second form of chance is thus unavoidable.

There is yet a third type of chance discussed by Poincaré that is prominently displayed in Clausewitz’s work. Poincaré argued that this kind is a result of our inability to see the universe as an interconnected whole:

Our weakness forbids our considering the entire universe and makes us cut it up into slices. We try to do this as little artificially as possible. And yet it happens from time to time that two of these slices react upon each other. The effects of this mutual action then seem to us to be due to chance.

Thus the drive to comprehend the world through analysis, the effort to partition off pieces of the universe to make them amenable to study, opens the possibility of being blind-sided by the very artificiality of the partitioning practice. This form of chance is a particularly acute problem when our intuition is guided by linear concepts.

Clausewitz has a profound sense of how our understanding of phenomena around us is truncated by the bounds we place on them for our analytical convenience. The assertion from On War quoted above, that “circumstances vary so enormously in war, and are so indefinable,” makes this point explicitly in the German original. A literal translation refers to the “diversity and indistinct boundary of all relationships” (“die Mannigfaltigkeit und die unbestimmte Grenze aller Beziehungen”) with which a commander must cope. Clausewitz repeatedly stresses the failure of theorists, such as his contemporaries Jomini and Bulow, to obtain effective principles because they insist on isolating individual factors or aspects of the problems presented in war. One indictment is particularly well known:

Efforts were therefore made to equip the conduct of war with principles, rules, or even systems. This did present a positive goal, but people failed to take an adequate account of the endless complexities involved. As we have seen, the conduct of war branches out in almost all directions and has no definite limits; while any system, any model, has the finite nature of a synthesis [in the sense of synthetic or man-made]. An irreconcilable conflict exists between this type of theory and actual practice…. [These attempts] aim at fixed values; but in war everything is uncertain, and calculations have to be made with variable quantities. They direct the inquiry exclusively toward physical quantities, whereas all military action is entwined with psychological forces and effects. They consider only unilateral action, whereas war consists of continuous interaction of opposites.

For Clausewitz, the generation of any system of principles for the conduct of war is a desirable goal but an unattainable one. Such an act of synthesis is indeed attractive, because it becomes so easy to forget the filters we have imposed on our view of the phenomenon.

But his concerns, like those of many scientists wrestling with nonlinear phenomena today, are open systems which cannot be isolated from their environments even in theory, which are characterized by numerous levels of feedback effects, and which need to be grasped realistically as an interactive whole. Traditional analysis that aimed at breaking the system into simpler parts fails now just as surely as it did in Clausewitz’s time, and for the same reasons. As Clausewitz writes of critical analysis and proof:

It is bound to be easy if one restricts oneself to the most immediate aims and effects. This may be done quite arbitrarily if one isolates the matter from its setting and studies it only under those conditions. But in war, as in life generally, all parts of the whole are interconnected and thus the effects produced, however small their cause, must influence all subsequent military operations and modify their final outcome to some degree, however slight. In the same way, every means must influence even the ultimate purpose. 

Interconnectedness and context, interaction, chance, complexity, indistinct boundaries, feedback effects and so on, all leading to analytical unpredictability—it is no wonder that On War has confused and disappointed those looking for a theory of war modeled on the success of Newtonian mechanics.

  

Alan Beyerchen, “Clausewitz, Nonlinearity and the Unpredictability of War,”

Unpredictability From Friction

“A key element of reality for Clausewitz is the ubiquity of “friction,” the “only concept that more or less corresponds to the factors that distinguish real war from war on paper.” This concept is usually interpreted as a form of “Murphy’s Law”: whatever can go wrong, will, and at the worst possible moment. That interpretation is not bad as far as it goes, but its presentation is usually skewed. The implication is that things go right until some exogenous factor ruins the situation. But for Clausewitz friction is neither extrinsic nor abnormal:”

Everything in war is simple, but the simplest thing is difficult. The difficulties accumulate and end by producing a kind of friction that is inconceivable unless one has experienced war….Countless minor incidents—the kind you can never really foresee—combine to lower the general level of performance, so that one always falls short of the intended goal…. The military machine—the army and everything related to it—is basically very simple and therefore seems easy to manage. But we should bear in mind that none of its components is of one piece: each part is composed of individuals,… the least important of whom may chance to delay things or somehow make them go wrong…. This tremendous friction, which cannot, as in mechanics, be reduced to a few points, is everywhere in contact with chance, and brings about effects that cannot be measured, just because they are largely due to chance.

The concept of friction is not just a statement that in war things always deviate from plan, but a sophisticated sense of why they do so. The analytical world, epitomized by the “frictionless pendulum” or the “perfectly spherical billiard ball on a frictionless surface” or “low-amplitude vibrations” so common in elementary physics, is one of linear rules and predictable effects. The real world and real war are characterized by the unforeseeable effects generated through the nonlinearity of interaction. 

“Friction” as used by Clausewitz entails two different but related notions that demonstrate the depth of his powers of observation and intuition. One meaning is the physical sense of resistance embodied in the word itself, which in Clausewitz’s time was being related to heat in ways that would lead ultimately to the Second Law of Thermodynamics and the concept of entropy. Friction is a nonlinear feedback effect that leads to the heat dissipation of energy in a system. The dissipation is a form of increasing degradation toward randomness, the essence of entropy. Even in peacetime, the degradation of performance in an army is a continual problem. In war, the difficulties are amplified. Military friction is counteracted by training, discipline, inspections, regulations, orders, and other means, not the least of which, according to Clausewitz, is the “iron will” of the commander. New energy and effort are sucked into the open system, yet things still never go as planned; dissipation is endemic due to the interactive nature of the parts of the system.

The second meaning of “friction” is the information theory sense of what we have recently come to call “noise” in the system. Entropy and information have some interesting formal similarities, because both can be thought of as measuring the possibilities for the behavior of systems. According to information theory, the more possibilities a system embodies, the more “information” it contains. Constraints on those possibilities are needed to extract signals from the noise. Clausewitz understands that plans and commands are signals that inevitably get garbled amid noise in the process of communicating them down and through the ranks even in peacetime, much less under the effects of physical exertion and danger in combat. His well-known discussion of the difficulty in obtaining accurate intelligence presents the problem from the inverse perspective, as noise permeates the generation and transmission of information rising upward through the ranks. From this perspective, his famous metaphor of the “fog” of war is not so much about a dearth of information as how distortion and overload of information produce uncertainty as to the actual state of affairs.

Clausewitz’s basic intuition here is that organizations are always slower and more inflexible than the natural events they are intended to control. Seen in this light, training, regulations, procedures, and so on are redundancies that enhance the probability of signal recognition through the noise. On the basis of linear assumptions, one expects major obstacles to produce proportionately serious errors in responding to the message. Clausewitz emphasizes, however, the disproportionately large role of the least important of individuals and of minor, unforeseeable incidents. “Friction” conveys Clausewitz’s sense of how unnoticeably small causes can become amplified in war until they produce macroeffects, and that one can never anticipate those effects. The issue is not just that “for want of a nail the shoe was lost….,” but that one can never calculate in advance which nail on which shoe will turn out to be critical. Due to our ignorance of the exact initial conditions, the cause of a given effect must, for all intents and purposes, often be treated as unavoidable chance.

 

Alan Beyerchen, “Clausewitz, Nonlinearity and the Unpredictability of War,”